How can I copy the base pose from hand rig to my hand rig?
Consider creating a pose library for the source armature. Assuming your destination armature has the same exact structure as the source one (same number of bones, same names) then this will work.
With the source armature selected, go into Pose Mode, then go to the Object Data tab of the Properties Panel. Expand the Pose Library section, and click New.

You now have a pose library, which can store any number of poses for your armature, but has no poses in it initially. So the field you now see will be empty. To the right of that empty field is a button containing a + sign.

Click it and and then choose Add New.

You should now see a pose listed in the previously empty field. It is called &quot;Pose&quot; by default.

The pose of your source armature is now stored as this listed entry. You can test this by changing the pose of your source armature, then going back to this Pose Library UI, making sure the appropriate pose is selected in the list (you must make sure your desired pose is the selected one in the list. It will often be the case that there is more than one pose in the list), and then click the Apply Pose Library Pose button, which contains a Magnifying Glass icon.

This will force the currently selected bones of the currently selected armature to take on the stored pose. It's important to remember that these stored poses can be applied on an individual bone basis, if desired. Only the selected bones will change to the stored pose. No UNselected bones will ever change. This can cause some strange results if one was unaware that some bones were unselected, while still wanting every bone in the armature to be affected by the stored pose. So it's important to know that this is how it works.
Once this pose is stored, you will need to apply it to the destination armature. To do this, you will need to select the destination armature in Object Mode, and then switch to Pose Mode. Select all the bones you want affected by the new pose (in your particular case, all of them). Now, return to the Pose Library section, which should still be open in the Properties Panel. You will notice that there appears to be no pose library anymore. Actually, it still exists, but your destination armature isn't linked to it yet. Your destination armature needs to be linked to the same pose library you already created before that library's poses can be applied to it. To link the pose library, click the weird looking link button immediately to the left of the &quot;New&quot; Button.

You will see the name of your pose library show up in the list (probably only one item displays in the list here, since you only have one pose library).

Click it, and it becomes linked to your armature. You should also now see the actual stored pose show up in the empty field below, as well. Make sure that this pose is selected, then click the Apply Pose Library Pose button (Magnifying Glass). Your pose has now been transferred to the destination armature.
You might ask why we would do things this way when setting all this up is so much more involved than simply using Copy and Paste. For one thing, Copy and Paste often doesn't work in Blender as we might expect. We can easily be led astray by our experience of how these features work in other programs, which can then lead to frustration. For two, by doing this, your poses are always safe, and can be reused repeatedly. It may seem like a lot to deal with to set it up, but a pose library is actually pretty useful once you get the hang of how it works.
Hope this helps.